Construction of the Generating Function of some Lie Superalgebras using Calogero-Sutherland Model

Abstract

Generating functions of characters for Lie superalgebras are used to derive important information such as branching rule, polynomial tensors, and many more. In this paper, we construct the generating function for the characters and dimensions of the basic Lie superalgebras osp(1, 2) using the supersymmetric Calogero-Sutherland model. The supersymmetric Calogero-Sutherland model is a quantum-integrable many body system which describes the interactions of particles moving on a circle. The interactions between these particles are determined by the root system of the chosen Lie superalgebra. The Lie superalgebra osp(1, 2) having dimension five and rank one has typical representation. Here we only present our detailed analysis on osp(1, 2).